Answer:
6 and -2
Explanation:
To find the possible values of n, we can use the distance formula between two points in a coordinate plane.
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
In this case, we are given the points (2, 1) and (n, 4), and the distance is 5 units. Plugging these values into the distance formula, we get:
5 = √[(n - 2)² + (4 - 1)²]
Simplifying the equation, we have:
25 = (n - 2)² + 9
25 = n² - 4n + 4 + 9
25 = n² - 4n + 13
Rearranging the equation, we have:
n² - 4n - 12 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring the equation, we have:
(n - 6)(n + 2) = 0
Setting each factor equal to zero, we get:
n - 6 = 0 or n + 2 = 0
Solving for n in each case, we find:
n = 6 or n = -2
Therefore, the possible values of n are 6 and -2.